I dont think you moving house has anything to do with this unless you cancelled and started as a new customer at your new property.
If you didn't do this then this might help to explain it:
https://www.sky.com/help/articles/been-overcharged
It sounds like the minimum term on your package has come to and end so the discount you had has now finished. When you took this out you would have been told how long it was going to last for so now is the time to call Sky to see if they will offer you a further discount for the next 12/18 months if you agree to a new contract.
If you have a Sky Mobile or Sky Talk landline phone then you can call Sky for free via the 150 number. Or under "Need more help ?" at the bottom this page is the number to call:
https://www.sky.com/help
Just ignore the messages at the start of the call and remain on the line for as long as you can and don't hang up when asked to do so.
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